Final answer:
Memory T cells help the body mount a rapid immune response by quickly producing large numbers of antigen-specific helper T cells upon re-exposure to an antigen.
Step-by-step explanation:
The type of T cell that helps an organism mount a rapid immune response is the Memory T cell. Memory T cells are long-lived and can respond quickly to secondary exposures to the same antigen. When a person is exposed to an antigen for the first time, some helper T cells become memory cells after the pathogen has been cleared. These memory cells are primed to produce large numbers of antigen-specific helper T cells rapidly if re-exposed to the same antigen, thus providing a swift and potent immune response.